Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
572 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#984 | C2 | semidirect |
| 3. C5×#5430 | C2 | semidirect |
| 4. C5×#5428 | C2 | semidirect |
| 5. C5×#5423 | C2 | semidirect |
| 13. C5×#984 | C22 | semidirect |
| 16. C5×GU(2,𝔽3) | C22 | semidirect |
| 17. #85542 | C5 | direct (N × H) |
| 41. C2×#984 | C2×C5 | semidirect |
| 42. #5430 | C2×C5 | semidirect |
| 43. #5428 | C2×C5 | semidirect |
| 44. #5423 | C2×C5 | semidirect |
| 99. #984 | C22×C5 | semidirect |
| 102. GU(2,𝔽3) | C22×C5 | semidirect |
| 421. C5 | #85542 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5945 | 2 |
| C2×C5×#984 | 2 |
| C5×#5430 | 2 |
| C5×#5428 | 2 |
| C5×#5423 | 2 |
| C5×#3022 | 3 |
| C5×#951 | 4 |
| #85542 | 5 |